Cooperate Without Looking
1
Suppose a friend asks you to proofread a
paper…
You hesitate while thinking about how big a pain
it is and say, “Hmm. Um. Well, OK.”
You’re a jerk even though you agreed.
2
Colleague asks you to attend his talk.
You ask, “how long will it last?” before agreeing
to attend.
You’re a jerk, whether you end up attending or
not.
3
In the first example, you hesitated as you
deliberated over whether it was worthwhile
In the second example, you asked for additional
information as you deliberated
Both reduce “kudos” for cooperation
Why?
4
Can reciprocity explain this?
Image courtesy of kjelljoran on Flickr. CC BY-NC-SA
5
In reciprocity, our behavior depends on others’
actions, not thought/search processes
Therefore, reciprocity cannot explain reduced
kudos from deliberating
6
So what is it?
7
Our intuition…
Cooperators who don’t deliberate, or “look”, can
be trusted to cooperate even when the
temptation to defect is high
8
Intuition is not enough…
9
Is the extra trust gained from not looking worth
the occasional high cost?
I.e., can cooperating without looking (CWOL) be
sustained as a Nash Equilibrium?
10
Can we get some new predictions or
prescriptions?
When do we expect people to care if their
colleagues “look”?
When do we expect colleagues to avoid looking?
11
Given that people don’t consciously choose
whether to look, can this behavior arise from
learning dynamics?
12
To deal with these question, we need formal
analysis
Proceed as follows…
13
1) Formally model this using “the envelope game”
2) Show “not looking” is an equilibrium in this game
3) Use this to find (simple, intuitive) conditions
under which to expect “care if look” and “avoid
looking”
4) Show “not looking” emerges in replicator
dynamic
14
Then use envelope game to gain insights into
less straightforward social phenomena:
-Flip-flopping politicians and “principled” people
-Why religions reward anonymous giving
-Taboo trade-offs
-Love
15
Let’s start with the model…
16
“The Envelope Game”
17
Two players
Play a repeated game
Each “stage” has four parts
18
First…
We model variation
in costs of cooperation
With probability p Low
Temptation “card”
is chosen and stuffed in
envelope
19
2
Second…
We model player 1’s
choice of whether
to “look”
1 chooses whether
or not to open the
envelope
Crucially we assume
others (player 2)
can observe
whether 1 looks
20
2
Third…
1 then chooses
whether or not to
Cooperate
2 is again able to
observe
21
2
And players receive
payoffs which depend
on the temptation
level and the choice
made by 1
Assumptions about payoffs:
> 0)
Both prefer Cooperative interaction to no interaction (a > 0, b
Cooperation is costly to 1 (c1 > a) and beneficial to 2 (b>d)
1 gains more from defecting in “high temptation” (c2 > c1)
22
Fourth and
finally…
Repeat
We model
others’ “trust” in
player 1
with probability w
Player 2 chooses
whether or not
to repeat the
interaction, with
discount w
23
Let’s take a second to think about strategies in this game…
A strategy for player 1 identifies whether she looks and whether she
cooperates in each round as a function of what has happened in the
past
E.g., In even rounds, don’t look, then cooperate. In odd rounds
look and defect
A strategy for player 2 identifies whether she continues or exits in each
round as a function of what has happened in the past
E.g., Continue if player 1 has never looked
24
And payoffs?
The ones we showed you are for one round. We need to
“add them up” across rounds
E.g., If player 1 look and cooperates when temptation is
low and player 2 continues if player 1 cooperates
Player 1’s payoffs: a/(1 – w)
Player 2’s payoffs: b/(1 – w)
25
Another example…
Suppose player 1 always defects and player 2
always exits
Player 1’s payoffs: c1p + c2(1-p)
Player 2’s payoffs: d
26
Let’s also take a second to think about the key assumptions…
Can avoid thinking about/gathering info about costs
Others can detect
How can others detect?
1’s reaction time?
The questions 1 asks 2?
27
One more important assumption:
Defection is so costly to player 2 that it’s not
worth interacting even if he only expects player
1 to only defect when the temptation is high
bp + d(1–p) < 0
28
Now ready to discuss results…
29
Main result:
1 Cooperates without looking (CWOL)
2 continues if 1 CWOL
is an equilibrium
when a/(1-w) > c1p + c2(1-p)
30
Sketch of proof:
For player 1, will not deviate (look or defect) as long
as payoff from future interaction is greater than
expected temptation, a/(1-w) > c1p + c2(1-p)
For player 2, if 1 isn’t looking, is no better off if
stops attending to looking and worse off if ends
interaction
31
So in response to our first set of questions…
Is the extra trust gained from not looking worth the
occasional high cost?
I.e., can cooperating without looking (CWOL) be
sustained as a Nash Equilibrium?
The answer is yes
32
Next we’d like to interpret the equilibrium condition to
answer our next set of questions…
Can we get some new predictions or prescriptions?
When do we expect people to care if their colleagues
“look”?
When do we expect colleagues to avoid looking?
But first…
33
There is another equilibrium where…
1 looks
2 cooperates if 1 cooperates (CWL)
when a/(1-w) > c2
34
Let’s compare these…
CWOL is an equilibrium when
a/(1-w) > c1p + c2(1-p)
CWL is an equilibrium when
a/(1-w) > c2
Since c2 > c1, CWOL is an equilibrium for a strictly
larger range of a’s
35
Combine the conditions above to get the condition where
CWOL is an equilibrium but CWL isn’t:
c1p + c2(1 p) < a/(1-w) < c2
This answers our questions: 2 will care if 1 looks and 1
will avoid looking when the expected gains from
defecting are small but the maximal gains are large
Notice: whether player 1 looks and 2 attends to looking
depends on the distribution of temptations (its average
and maximum), not the realized temptation in a given
period
36
It also teaches us that the ability to avoid
looking and to detect looking enables
cooperation when otherwise wouldn’t be
possible
37
Summary so far…
We have shown CWOL is an equilibrium
And interpreted equilibrium condition to learn
when not looking and attending to looking are
important
38
But no one is consciously choosing to not look or to
attend to looking
Instead, use feelings, heuristics or ideologies which
guide them when to look and when to attend to
looking
I.e.,
I respect “principled” people
I can’t fathom trading lives for money
39
Without rationality, need another justification
for Nash
So we use dynamics
Why? Dynamics describe simple processes of
imitation, learning, or evolution, where
rationality not needed
40
As usual, only assumption… more successful
strategies become more frequent
(e.g. because more likely to be imitated)
41
R
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R
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R
T=0
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L
R
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L
R
L
L
R
L
L
L
L
L
L
L
L
T=1
T=2
T=3
L
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42
Of course strategies aren’t imitated
Feelings/heuristics/ethics/ideologies are
But these are just ways of implementing
strategies, so we represent them by the strategy
they implement
43
The dynamic we use is replicator dynamic
For replicator, we need to simplify strategy
space…
44
For each player, we use the following strategies
45
We also need to be a little more complete in
classifying equilibria
46
Here are the two we identified before
There’s also a third one which is always an equilibrium
47
Now we lump
together ones which
are “behaviorally
identical”
For example, in
CWOL, as long as
enough 2s exit if look
it doesn’t matter if
some 2s exit if defect
48
Here’s how the simulation works
49
For each of many parameter values…
For each of 5,000 trials…
We seed the population with random
mixtures of strategies
Then wait for the population to stabilize
Then classify the outcome
50
We find…
Population ends up at CWOL fairly often in
parameter region where it is an equilibrium
51
52
And that answered our third set of questions
Given that people don’t consciously choose
whether to look, can this behavior arise in
dynamics?
The answer is yes
53
Let’s apply these results to a few interesting
social phenomena…
54
First one… “flip-flopping” politicians
55
I was for
the military
before I was
against it.
Image is in the public domain.
56
Why is “flip-flopping” bad?
Isn’t it better for Kerry to be sensitive to
constituents’ opinion?
57
This is part of a general question…
Kerry decides policy “strategically” and not based
on “principles”
Why do we like people who have “principles” and
not those who are “strategic”?
And when will we particularly care?
58
CWOL provides the following possible
explanation…
59
Kerry (re)decides political stance after
calculating costs to his career
So he cannot be trusted to make good policy
when it would hurt his career
60
This generalizes to strategic vs. principled people more
generally
And we can use our equilibrium condition to identify
when we will especially care that people are principled
When usually have fairly aligned incentives but are rare
occasions that could benefit them and harm us
E.g., crucial that girlfriend/boyfriend is principled, but not
that drinking buddy is
61
Any evidence?
62
Second puzzle… Why do religions reward
anonymous giving?
For example…
63
Maimonides’ Eight Levels of Giving
8. He who does not give enough—and even that unwillingly.
7. He who does not give enough—but what he gives, he gives graciously.
6. He who gives enough—but only after he is asked.
5. He who gives enough and before he is asked—but with both parties knowing
each other.
4. He who gives and does not know who receives—but the recipient knows who
gave it.
3. He who gives and knows who will receive it—but the recipients will not know
who gave it.
2. He who gives without knowing who will receive—and without the recipient
knowing who gave it.
1. He who gives—and also assists the recipient in addressing the reason for the
need in the first place.
64
Do you know of examples from other religions?
65
Why reward anonymity and not just giving?
An anonymous gift can feed no more starving
children
66
More generally,
Why do we admire givers more when they give
anonymously?
For example…
67
See article about Steve Jobs’ philanthropy.
Source: UK Daily Mail, May 24, 2013
68
We argue that anonymous giving is more honorable
because such people are giving without “looking” at
the reputational benefits
So they can be expected to continue giving, even
when the reputational effects are minimal
(Note here it is benefits not temptations, but works
the same)
69
But people typically know they’re giving
anonymously
Might be guided by principles to do so anyway
70
Suggests trade-off between giving so everyone
knows and admires a little, and a few people
might find out and admire a lot
71
Third puzzle… taboo tradeoffs
72
What is a taboo trade-off?
Let’s illustrate with an example…
73
A third of Medicare dollars are spent in the last
month of life
(Source: http://www.forbes.com/sites/michaelbell/2013/01/10/why-5-of-patients-create-50-of-health-care-costs/)
Presumably, for a lot of folks, we know those dollars
are unlikely to help
And those dollars could be used to more effect
elsewhere… for example, to improve the other 959
months of our lives
74
But if you ask a doctor, they can’t even imagine
making this trade-off
75
As Tetlock and Roth point out…
We find it “disgusting” to even consider trading
off money against life
I.e., it’s “taboo”
76
Note that this taboo is governed by emotions or
ideologies—most people have not consciously
considered it
And that it is upheld despite enormous costs
Suggests psychologically deep
77
This generalizes…
We find it disgusting to even consider trading off money with
many “sacred” goods
We ask:
Why?
Which goods are liable to be sacred?
Should we, as a society, respect taboos?
78
Here’s our suggestion for why and when…
We find such tradeoffs disgusting because they signal a willingness to
look at the benefits of defecting…
… in domains where rare instances of huge potential temptations
E.g.,
-If partner considers selling sex, then might cheat when the
right person comes along
-If caretaker put a price tag on life, might compromise it for
especially lucrative offer
79
Policy implication:
While politicians might want to signal that they
would never trade lives for money
Gains from appearing trustworthy accrue to the
politicians while costs accrue to us
We need a government that surmounts taboos to
tackle these admittedly hard-to-fathom questions
80
Any evidence to support this claim?
How about evidence to support our prediction
on which items will be sacred?
81
Last puzzle… Intuitive cooperation
82
First piece of background…
Psychologists sometimes discuss two “types” of
decisions:
System 1: intuitive
System 2: deliberate
83
Second piece of background…
People cooperate intuitively
Cooperators have faster response time
than defectors
When forced to slow down, cooperate less
84
Reprinted by permission from Macmillan Publishers Ltd: Nature.
Source: Rand, David G., Joshua D. Greene, et al. “Spontaneous Giving
and Calculated Greed.” Nature 489 (2012): 427-30. © 2012.
Source: Rand et al. 2012
85
Why would people cooperate intuitively?
Our model suggests that intuitive cooperation
might be a way of not looking
If some lab subjects not looking, and some
looking, then, on average, cooperators decide
faster
86
Gives two novel predictions:
Especially likely to be intuitive in cooperative
situations
Others will prefer to interact with intuitive
than deliberative cooperators
Any ideas for how to test?
87
Let’s summarize…
88
People attend to whether cooperators deliberate.
Reciprocity can’t explain this
We use simple model and dynamics to show that when
can detect looking, sometimes worth not looking
That sometimes: when relationship is beneficial on
average but there are occasional large temptations
Possibly explains puzzling social behaviors
89
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14.11 Insights from Game Theory into Social Behavior
Fall 2013
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